RACIAL HISTORY: Trayvon Martin (above), the “beer summit” and a prison tower will be part of a new African-American museum. Photo: Family photo/Splash News

(Pete SouzaWhite House Press)

(National Museum of African American History)

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A director at the Smithsonian Institution wants to stock a new addition to the national museum complex with a controversial piece of recent US history — Trayvon Martin’s hoodie.

Lonnie Bunch said that once the legal case plays out, he’d love to have the gray hooded sweat shirt the unarmed 17-year-old was wearing the night he was fatally shot by George Zimmerman in Sanford, Fla.

Martin’s hoodie would provide an opportunity to further the discussion about race in America, Bunch said.

“It became the symbolic way to talk [about] the Trayvon Martin case. It’s rare that you get one artifact that really becomes the symbol,” Bunch said.

“Because it’s such a symbol, it would allow you to talk about race in the age of Obama.”

Bunch, director of the Smithsonian’s National Museum of African American History and Culture, now under construction in Washington, DC, has assembled other controversial pieces about race relations throughout US history.

One example is a guard tower from Louisiana’s notorious Angola State Penitentiary.

Another is the handcuffs used to restrain Harvard professor Henry Louis Gates Jr. in an episode that sparked a national debate about race and led to a “beer summit” with President Obama aimed at easing tensions.

Bunch also wants the hoodie that Marian Wright Edelman, founder of the Children’s Defense Fund, wore in solidarity with anti-Zimmerman protesters.

“Are we in a postracial age?” Bunch asked, dreaming about how the hoodie might help shape perceptions. Then he answered the question: “This trial [of George Zimmerman in Martin’s death] says, ‘No.’ ”

The museum is expected to open in 2015.

Its not clear if the hoodie is available. Since the verdict, its been shuffled from one place to another.

Prosecutors first passed it to the Sanford Police Department.

But it is now apparently in the hands of the US Justice Department, which is weighing a civil-rights case against Zimmerman.

Last week, Sanford police packed boxes of evidence — including the Skittles and an AriZona fruit drink Martin was carrying when he was slain on Feb. 26, 2012 — and drove them to a Justice Department office in Orlando.

Meanwhile, Zimmerman’s bizarre post-acquittal wanderings took another turn yesterday. After helping save a family from a car wreck on a road in Florida last month, he was pulled over Sunday for speeding near Dallas and the encounter was captured on dashcam video.

He and admitted he had a legal handgun in the glove compartment, and was not ticketed.